**Riemannian wavefield extrapolation:**- In rwe, I extend one-way wavefield extrapolation to a general coordinate framework which can be described using Riemannian geometry. Such natural coordinates allow for accurate wave propagation in arbitrary directions (95), in contrast with conventional downward continuation which favors waves propagating vertically. A special case of Riemannian coordinates is represented by ray coordinates obtained by ray tracing in a smooth background medium. This method can be used for imaging of steeply dipping reflectors or overturning reflections.
**Angle-domain common image gathers:**- In adcig, I present a method for constructing angle-domain common image gathers (reflectivity function of scattering angle) from images obtained by wavefield extrapolation. The method described in this thesis operates in the image space, which enables transformations between the angle and offset domains without data remigration. Since the transformation to the angle-domain is separated from the migration itself, this method can be used to construct angle gathers for shot-geophone migration (94), for shot-profile migration (78), for converted waves (83), and for reverse-time imaging (11). The method can also be used for AVA studies (90), for multiple suppression after migration (96), or for migration velocity analysis (wemva).
**Prestack Stolt residual migration:**- In storm, I extend to the prestack domain the residual migration method introduced by (102). Residual migration produces images corresponding to velocities described by a scalar ratio relative to the velocity of the original migration (87). The method is formulated in the Fourier domain, therefore it is fast and robust. I use this residual migration method for constructing image perturbations for wave-equation migration velocity analysis (wemva).
**Wave-equation migration velocity analysis:**- In wemva, I present the theory of migration velocity analysis using wavefield extrapolation (88). This velocity analysis method inherits the characteristics of wavefield extrapolation, mainly robustness in presence of large and sharp velocity contrasts, bandlimited model sensitivity and multipathing. The velocity updates are derived from image perturbations using a linearized operator based on the first-order Born approximation. The image perturbations are constructed based on focusing or moveout information measured on angle-domain common image gathers (adcig), using a linearized version of prestack residual migration (storm).
**Examples:**- In example, I present examples of wave-equation migration velocity analysis. An important application is for subsalt imaging (89), where ray-based methods often fail. I demonstrate that wave-equation migration velocity analysis is capable of updating velocity subsalt, since it inherits the robustness and accuracy of the underlying wavefield extrapolation technique. I define prestack image perturbations based on angle-domain common image gathers (adcig) and residual migration (storm). Another important application is for velocity analysis using diffracted data (1). In this application, I define image perturbations based only on spatial focusing information obtained using residual migration (storm).

11/4/2004